Planes are unlike other sorts of transportation in that their energy consumption is pretty closely proportional to their weight, because they are constantly spending energy throwing air downward to support their weight, so the low energy densities of rechargeable batteries are very unappealing for long-distance flight. Plausible alternatives include airships, ultra-low-stall-speed planes like gliders and Burt Rutan's Voyager, aluminum-air batteries, and synfuel. Of course, short-distance planes are already going electric with Joby.
Ships, we'll see. Most shipping ships are container ships (as opposed to, say, tankers, cruse ships, or ship shipping ships shipping shipping ships), and those are already slow enough that a substantial part of world trade is by airplane now, because inventory on a container ship is inventory you can't sell yet, or at least can't deliver yet. You could imagine a future where container ships are partly powered by onboard sails and partly powered by giant lightweight solar farms towed behind them on hydrofoils, but I don't think we're going to see container ships powered by lithium-ion batteries. Aluminum-air, maybe.